Appendix A. SYSTAT output for backwards stepwise multiple regression. Response = depth of giant kelp shallow limit (in meters); OD = wave orbital displacement (in meters); BD = wave breaking depth (in meters); LTD = average tidal height (in meters); W = wind velocity (in meters/s). Backwards stepwise multiple regression was run using MGLH:REGRESSION under the STATS menu in SYSTAT 5.2 for Macintosh. Response was the dependent variable; CONSTANT, OD, BD, LTD, and W were the dependent variables; Stepwise was set to custom, with a backwards step order, and P = 0.15 to remove. Only standard SYSTAT output is presented.
Backwards
stepwise variable selection
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DEPENDENT VARIABLE: RESPONSE | |
MINIMUM TOLERANCE FOR ENTRY INTO MODEL = 0.010000 |
Initial
model
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STEP #0; R= 0.775; RSQUARE= 0.601 | ||||||
IN | ||||||
--- | ||||||
VARIABLE |
COEFF
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SE
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STD COEF
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TOLER
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F
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P
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1 CONST | ||||||
2 OD |
0.1433
|
0.046
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0.55
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0.38836
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9.57
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0.0040
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3 BD |
-0.0042
|
0.021
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-0.03
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0.42462
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0.04
|
0.8402
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4 LTD |
-0.0596
|
0.142
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-0.05
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0.85087
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0.17
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0.6791
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5 W |
0.0079
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0.004
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0.30
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0.47748
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3.57
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0.0677
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OUT | PART. CORR | |||||
--- | ||||||
none |
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1st variable
removal
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STEP #1; R= 0.775; RSQUARE= 0.600 | ||||||
TERM REMOVED: BD | ||||||
IN | ||||||
--- | ||||||
VARIABLE |
COEFF
|
SE
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STD COEF
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TOLER
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F
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P
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1 CONST | ||||||
2 OD |
0.1384
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0.038
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0.53
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0.53399
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13.0
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0.0011
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4 LTD |
-0.0553
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0.139
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-0.05
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0.87021
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0.16
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0.6938
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5 W |
0.0077
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0.004
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0.29
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0.50605
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3.69
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0.0629
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OUT |
PART. CORR
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--- | ||||||
3 BD |
-0.035
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N/A
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N/A
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0.42462
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0.04
|
0.8402
|
2nd variable
removal
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STEP #2; R= 0.773; RSQUARE= 0.598 | ||||||
TERM REMOVED: LTD | ||||||
IN | ||||||
--- | ||||||
VARIABLE |
COEFF
|
SE
|
STD COEF
|
TOLER
|
F
|
P
|
1 CONST | ||||||
2 OD |
0.1392
|
0.038
|
0.53
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0.53564
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13.0
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0.0009
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5 W |
0.0081
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0.004
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0.31
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0.53564
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4.41
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0.0431
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OUT | PART. CORR | |||||
--- | ||||||
3 BD |
-0.025
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N/A
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N/A
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0.43420
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0.02
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0.8861
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4 LTD |
-0.068
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N/A
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N/A
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0.87021
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0.16
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0.6938
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THE SUBSET
MODEL INCLUDES THE FOLLOWING PREDICTORS:
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CONSTANT | ||||||
D | ||||||
W | ||||||
Parameterization
of final model
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DEP VAR: RESPONSE N: 38; MULTIPLE R: 0.773; SQUARED MULTIPLE R: 0.598; ADJUSTED SQUARED MULTIPLE R: 0.575;STANDARD ERROR OF ESTIMATE: 0.139 | ||||||
VARIABLE |
COEFF
|
SE
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STD COEF
|
TOLER
|
F
|
P
|
CONST |
2.873
|
0.097
|
0.00
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N/A
|
30.0
|
0.0000
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OD |
0.139
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0.038
|
0.53
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0.53564
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3.62
|
0.0009
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W |
0.008
|
0.004
|
0.31
|
0.53564
|
2.10
|
0.0431
|
Analysis
of variance
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SOURCE |
SS
|
DF
|
MS
|
F
|
P
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|
REGRESSION |
1.012
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2
|
0.51
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26.06
|
0.0000
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RESIDUAL |
0.679
|
35
|
0.02
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